Computing the exact Wasserstein distance, however, is computationally expensive and usually is solved by a linear program (Appendix A and D ). [1]} introduced an interesting method which relaxes the OT problem using the entropy of the solution as a strong convex regularizer. The entropic regularization provides two main advantageous: 1) The regularized OT problem relies on Sinkhorn’s algorithm [2]} that is faster by several orders of magnitude than the exact solution of the linear program. 2) In contrast to exact OT, the regularized OT is a differentiable function
of their inputs, even when the OT problem is used for discrete measures. These advantages have caused that the regularized OT to receive a lot of attention in machine learning applications such as generating data [3]}, [4]}, designing loss function [5]}, domain adaptation [6]}, [7]}, clustering [8]}, [9]}, [10]} and low-rank approximation [11]}.
